(1) Field of the Invention
The invention relates generally to the field of digital filters and more particularly to adaptive IIR (infinite impulse response), or recursive, filters.
(2) Description of the Prior Art
Digital filters are used in a number of applications. In some applications, digital filters facilitate the extraction of data from an otherwise noisy input signal.
In other applications, to which the instant invention is primarily directed, the digital filter is used in connection with a reference system, which receives an input signal and generates an output signal in response thereto. In such applications, the digital filter is used to facilitate an the understanding of the operation of a reference system. Digital filters used in such applications are referred to as "adaptive filters", because they operate in response to filter parameters that can be modified by the filters themselves to conform the operation of the filter to the operation of the reference system.
FIG. 1 depicts a general block diagram illustrating a system including an adaptive digital filter. With reference to FIG. 1, the system includes the reference system module 10 and the adaptive filter system 11, both of which receive an input signal u(t) in parallel. In the following, "t" represents a continuous variable, such as time; however, adaptive filter systems similar to those described in the following may be used with non-continuous input data, such as time-sampled data, with extensions that will be apparent to those skilled in the art. The reference system module generates an output signal, identified as reference signal y(t). The adaptive filter system 11 includes a programmable filter module 12 and a parameter adjustment module 13. The programmable filter module 12 receives the input signal u(t) and generates in response thereto and in response to various filter parameters, an output filtered signal y'(t). The reference signal y(t) generated by the reference system module 10, and the filtered signal y'(t) generated by the programmable filter module 12, are both directed to an adder 13, which generates an error signal v(t) as the difference between the reference signal y(t) and the filtered signal y' (t), or EQU v(t)=y(t)-y'(t) (1)
which is directed to a parameter adjustment module 14. The parameter adjustment module 14 receives the error signal v(t), and also the filter parameters and generates in response parameter adjustment values that are coupled to the programmable filter module 12 to adjust the parameters of the module 12. The parameter adjustment module 14 generates the parameter adjustment values to minimize the value of the error signal v(t), that is, to provide that the filtered signal y'(t) generated by the programmable filter module 12 maintains a close relationship to the reference signal y(t) from the reference system module 10. To the extent that the parameter adjustment module 14 can adjust the filter parameters of the programmable filter module 12 to minimize the error signal v(t), the operation of the programmable filter module 12 will constitute a good model of the operation of the reference system module 12 in response to the input signal u(t).
There are two basic types of digital filter design methodologies, namely, non-recursive, or "finite impulse response" ("FIR"), filters, and recursire, or "infinite impulse response" ("IIR") filters. In an FIR filter, the output signal Y'FIR (t) is essentially a polynomial in the input signal u(t), or ##EQU1## where the coefficients c are the filter parameters. It will be appreciated that, for an FIR filter, the value of the output signal y'.sub.FIR (t) is linear in each of the coefficients c.sub.i. On the other hand, in an IIR filter, the output signal Y'.sub.IIR (t) is a ratio of polynomials in the input signal u(t), or ##EQU2## with coefficients a.sub.j and b.sub.k being the filter parameters. It will be apparent that the output signal y'.sub.IIR (t) will not be linear in the coefficients a.sub.j and b.sub.k, in which case adjustment of the filter parameters in relation to the error signal v(t) can be a complex matter.